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Updated: Jul 4, 2026

A Simple Planting Technique for Re-establishing Trees Where Frequent Inundation Occurs

A Simple Planting Technique for Re-establishing Trees Where Frequent Inundation Occurs

Published on: January 26, 2018

Invasion percolation through minimum-weight spanning trees.

Roland Glantz¹, Markus Hilpert

¹Department of Geography and Environmental Engineering, The Johns Hopkins University, 313 Ames Hall, 3400 North Charles Street, Baltimore, Maryland 21218-2686, USA. roland_glantz@jhu.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 4, 2008

Summary

This study simplifies complex pore network simulations by using minimum-weight spanning trees. This approach optimizes invasion percolation for drainage and imbibition processes, reducing computational time.

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Area of Science:

Pore network modeling
Multiphase flow simulation
Computational physics

Background:

Invasion percolation is a standard method for simulating capillary-dominated processes in porous media.
Existing methods link invasion percolation to minimum-weight spanning trees, but extensions to other percolation types and complex phenomena were limited.

Purpose of the Study:

To mathematically justify the two-step minimum-weight spanning tree approach for invasion bond percolation.
To extend this efficient method to invasion site percolation.
To incorporate trapping and snap-off phenomena into the simulation framework for enhanced accuracy.

Main Methods:

Formulation of the minimum-weight spanning tree property underpinning the two-step approach.
Extension of the two-step method to invasion site percolation models.
Integration of trapping (drainage) and snap-off (imbibition) into the simulation.

Main Results:

The study provides a rigorous formulation for the minimum-weight spanning tree justification.
The two-step approach is successfully extended to invasion site percolation.
The enhanced method efficiently simulates drainage and imbibition, including trapping and snap-off.

Conclusions:

The minimum-weight spanning tree approach significantly optimizes invasion percolation simulations.
This unified method achieves a time complexity of O(mα(m,n)) for various pore network simulations.
The findings enable faster and more accurate modeling of multiphase flow in porous media.